Factor Indeterminacy as Metrological Uncertainty: Implications for Advancing Psychological Measurement

Abstract

Researchers have long been aware of the mathematics of factor indeterminacy. Yet, while occasionally discussed, the phenomenon is mostly ignored. In metrology, the measurement discipline of the physical sciences, uncertainty – distinct from both random error (but encompassing it) and systematic error – is a crucial characteristic of any measurement. This research argues that factor indeterminacy is uncertainty. Factor indeterminacy fundamentally threatens the validity of psychometric measurement, because it blurs the linkage between a common factor and the conceptual variable that the factor represents. Acknowledging and quantifying factor indeterminacy is important for progress in reducing this component of uncertainty in measurement, and thus improving psychological measurement over time. Based on our elaborations, we offer a range of recommendations toward achieving this goal.

Keywords:

• Structural equation modeling
• factor indeterminacy
• validity
• measurement models

Article Information

Conflict of interest disclosures: Each author signed a form for disclosure of potential conflicts of interest. Jan-Michael Becker is a co-developer and co-founder of SmartPLS (www.smartpls.com). SmartPLS is a statistical software for modeling and analyzing partial least squares path models. The other authors did not report any financial or other conflicts of interest in relation to the work described.

Ethical principles: The authors affirm having followed professional ethical guidelines in preparing this work. These guidelines include obtaining informed consent from human participants, maintaining ethical treatment and respect for the rights of human or animal participants, and ensuring the privacy of participants and their data, such as ensuring that individual participants cannot be identified in reported results or from publicly available original or archival data.

Funding: This work was not supported.

Role of the funders/sponsors: None of the funders or sponsors of this research had any role in the design and conduct of the study; collection, management, analysis, and interpretation of data; preparation, review, or approval of the manuscript; or decision to submit the manuscript for publication.

Acknowledgments: The authors thank Donald Schopflocher, Keith Markus, three exceptional reviewers and the editors for their comments on prior versions of this manuscript. The ideas and opinions expressed herein are those of the authors alone, and endorsement by the authors’ institutions is not intended and should not be inferred.

Notes

1 Here, parameter estimates replace population values as necessary.

2 We thank the associate editor for pointing us to this important reference.

3 Note that rotational indeterminacy and factor indeterminacy are not the same thing. Factor indeterminacy will remain even if all model parameters are fixed at particular values and the entire solution is thus fixed, as long as the rank problem remains.